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• Reasoning/Sense Making/Proof
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## Improving Preservice Secondary Mathematics Teachers' Capability With Generic Example Proofs

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

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## Mysterious Subtraction

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

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## Arithmogons

Easy-to-design puzzles that encourage mathematical reasoning and promote numerical fluency, arithmogon puzzles are simple: Add the numbers in two circles to get the number in the square. Every month, this final page of the journal highlights a quick game, puzzle, activity, or instructional strategy and suggestions for teachers of different grade bands to use the idea in the classroom.

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## Everybody, SCATteR

Skip counting around the room (SCATR) is a strategy that promotes numerical fluency and attention to number relationships. Variations of SCATR for students in K'grade 6 are shared.

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## Capturing Thinking on the Talk Frame

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.

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## A Pathway for Mathematical Practices

See how the NCTM Process Standards in action integrate Common Core State Standards in a second-grade classroom.

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## Pattern-block frenzy

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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## A Little Area Challenge: A Sod Story

Implement this professional development workshop designed to help teachers excavate the concept of area, uncover misconceptions, and cultivate understanding.

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## A Super Way to Soak in Linear Measurement

After analyzing advertising claims regarding water shooters, students present their findings.

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## Fluency with Basic Addition

Applying known facts to derive unknown facts results in efficiency, flexibility, and an understanding of number combinations for young students.